Expression of type Lambda

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, k, t
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Interval, Mult, NaturalPos, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, _psi_t_ket, two_pow_t

# build up the expression from sub-expressions
expr = Lambda(t, Conditional(Equals(_psi_t_ket, ScalarMult(frac(one, Exp(two, frac(t, two))), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t)), domain = Interval(zero, subtract(two_pow_t, one))))), InSet(t, NaturalPos)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

t \mapsto \left\{\lvert \psi_{t} \rangle = \left(\frac{1}{2^{\frac{t}{2}}} \cdot \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)\right) \textrm{ if } t \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 59 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 30 operands: 6
4	Literal
5	ExprTuple	7, 8
6	ExprTuple	59, 9
7	Operation	operator: 10 operand: 59
8	Operation	operator: 28 operands: 12
9	Literal
10	Literal
11	ExprTuple	59
12	ExprTuple	13, 14
13	Operation	operator: 26 operands: 15
14	Operation	operator: 16 operand: 19
15	ExprTuple	60, 18
16	Literal
17	ExprTuple	19
18	Operation	operator: 54 operands: 20
19	Lambda	parameter: 51 body: 22
20	ExprTuple	58, 23
21	ExprTuple	51
22	Conditional	value: 24 condition: 25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	ExprTuple	59, 58
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	51, 34
32	Operation	operator: 54 operands: 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	ExprTuple	40, 41
36	Literal
37	ExprTuple	51, 59
38	Literal
39	ExprTuple	42, 43
40	Literal
41	Operation	operator: 44 operands: 45
42	Literal
43	Operation	operator: 46 operands: 47
44	Literal
45	ExprTuple	58, 48, 49, 50, 51
46	Literal
47	ExprTuple	52, 53
48	Literal
49	Literal
50	Literal
51	Variable
52	Operation	operator: 54 operands: 55
53	Operation	operator: 56 operand: 60
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	60
58	Literal
59	Variable
60	Literal